### Abstract

In this paper, we consider three versions of semi-online hierarchical scheduling problems on two identical machines, with the purpose of minimizing the makespan. In the first version, we assume that the total size of jobs with lower hierarchy is given and we get the tight bound (Formula presented.). In the second one, assume that the total size of jobs in each hierarchy is given and we get the tight bound (Formula presented.). In the third one, we assume that the total size of jobs with lower hierarchy is known in advance and a buffer of size K is given to store at most K jobs temporarily. We propose an optimal algorithm with competitive ratio (Formula presented.) using K=1 and show that a bigger buffer size is not helpful.

Original language | English |
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Pages (from-to) | 873-881 |

Number of pages | 9 |

Journal | International Journal of Computer Mathematics |

Volume | 92 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 4 2015 |

### Keywords

- competitive ratio
- hierarchical constraint
- scheduling problem
- semi-online

### ASJC Scopus subject areas

- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

*International Journal of Computer Mathematics*,

*92*(5), 873-881. https://doi.org/10.1080/00207160.2014.922682